F/D is purely geometric. Once you know any two of diameter, focal length, or depth, you can calculate it.
Definitions: D = dish diameter
f = focal length (vertex to focus)
d = dish depth (rim to vertex)
F/D = f / D
Key parabolic dish formula:
f = D^2 / (16 d)
So:
F/D = D / (16 d)
How to calculate in practice
Method 1: Diameter and depth known (most common)
- Measure: D = dish diameter
d = dish depth (straightedge across rim, measure down to centre) - Calculate: F/D = D / (16 d)
Example: D = 3.0 m
d = 0.45 m
F/D = 3.0 / (16 x 0.45) = 0.42
Method 2: Focal length known
F/D = f / D
Method 3: Using rim angle (half-angle theta)
F/D = 1 / (4 * tan(theta / 2))
Typical values: Deep TV dishes: F/D ~ 0.35
Prime-focus dishes: F/D ~ 0.35 to 0.45
Offset dishes: F/D ~ 0.55 to 0.65
Why F/D matters
Low F/D (deep dish):
- Wide feed beam
- Higher spillover risk
High F/D (shallow dish):
- Narrow feed beam
- Better efficiency
For L-band (1420 MHz), prime-focus dishes usually work best around: F/D ~ 0.4 to 0.45